The so-called Air Quality Index (AQI), expresses the quality of atmospheric air. The overall AQI is determined from the AQIs of some reference air pollutants, which are calculated by a transform of the respective concentrations. Concentrations of air pollutants are compositional data; they are expressed as part of mass of each pollutant in a total air volume or mass. Therefore, air pollution concentration data, as compositional data, just provide ratio information between concentrations of pollutants. Operations involved in the computation of overall AQI are not admissible operations in the framework of compositional data analysis, as they destroy the original ratio information. Consequently, the standard methodology should be reviewed for such calculations, taking into account the principles and operations of compositional data analysis. The objective of this article is to present a first approach to incorporate compositional perspective to air quality expression. For this, it is proposed to use a balance log-contrast of concentrations expressed in µg/m3 to define a new kind of air quality indicator. Furthermore, the geometric mean of the concentrations is applied to obtain a new and simple scale air quality index, avoiding definition of piecewise linear interpolations used in the standard AQI computation. As an illustrative example, statistical analysis of atmospheric pollution data series (2004–2013) of the city of Madrid (Spain) has been carried out.

The final publication is available at Springer via http://dx.doi.org/10.1007/s11004-015-9599-5

General systems are frequently decomposable into parts and these parts can evolve in time or space, a frequent occurrence in the field of Geosciences. In most cases, fitting models to forecast future states of the system is a goal of the analysis. Modelling interactions between parts may also be of common interest. The system can be analysed from different points of view; the traditional one consists in modelling each part of the system in time. Alternatively, modelling the evolution of the parts as proportions is proposed herein and attention is centred on the compositional evolution. The compositions are expressed in orthogonal coordinates (ilr) and then modelled using first-order differential equations with constant coefficients. Simple models are shown to be very flexible, including many of the standard growth curve models. The models are fitted using regression techniques on the integrated coordinates. The use and interpretation of these differential models is illustrated with several examples: a simulated example; urban waste in Catalonia (Spain); oil production and reserves; and growth of a luzonite crystal

A model for generating daily spatial correlated rainfall fields suitable for evaluating the impacts of climate change on water resources is presented. The model, termed Stochastic Rainfall Generating Process, is designed to incorporate two major nonstationarities: changes in the frequencies of different precipitation generating mechanisms (frontal and convective), and spatial nonstationarities caused by interactions of mesoscale atmospheric patterns with topography (orographic effects). These nonstationarities are approximated as discrete sets of the time-stationary Stochastic Rainfall Generating Process, each of which represents the different spatial patterns of rainfall (including its variation with topography) associated with different atmospheric circulation patterns and times of the year (seasons). Each discrete Stochastic Rainfall Generating Process generates daily correlated rainfall fields as the product of two random fields. First, the amount of rainfall is generated by a transformed Gaussian process applying sequential Gaussian simulation. Second, the delimitation of rain and no-rain areas (intermittence process) is defined by a binary random function
simulated by sequential indicator simulations. To explore its applicability, the model is tested in the Upper Guadiana Basin in Spain. The result suggests that the model provides accurate reproduction of the major spatiotemporal features of rainfall needed for hydrological modeling and water resource evaluations. The results were significantly improved by incorporating spatial drift related to orographic precipitation into the model.

A model for generating daily spatial correlated rainfall fields suitable for evaluating the impacts of climate change on water resources is presented. The model, termed Stochastic Rainfall Generating Process, is designed to incorporate two major nonstationarities: changes in the frequencies of different precipitation generating mechanisms (frontal and convective), and spatial nonstationarities caused by interactions of mesoscale atmospheric patterns with topography (orographic effects). These nonstationarities are approximated as discrete sets of the time-stationary Stochastic Rainfall Generating Process, each of which represents the different spatial patterns of rainfall (including its variation with topography) associated with different atmospheric circulation patterns and times of the year (seasons). Each discrete Stochastic Rainfall Generating Process generates daily correlated rainfall fields as the product of two random fields. First, the amount of rainfall is generated by a transformed Gaussian process applying sequential Gaussian simulation. Second, the delimitation of rain and no-rain areas (intermittence process) is defined by a binary random function simulated by sequential indicator simulations. To explore its applicability, the model is tested in the Upper Guadiana Basin in Spain. The result suggests that the model provides accurate reproduction of the major spatiotemporal features of rainfall needed for hydrological modeling and water resource evaluations. The results were significantly improved by incorporating spatial drift related to orographic precipitation into the model.

Tritium is a short-lived radioactive isotope (T 1/2=12.33 yr) produced naturally in the atmosphere by cosmic radiation but also released into the atmosphere and hydrosphere by nuclear activities (nuclear power stations, radioactive waste disposal). Tritium of natural or anthropogenic origin may end up in soils through tritiated rain, and may eventually appear in groundwater. Tritium in groundwater can be re-emitted to the atmosphere through the vadose zone. The tritium concentration in soil varies sharply close to the ground surface and is very sensitive to many interrelated factors like rainfall amount, evapotranspiration rate, rooting depth and water table position, rendering the modeling a rather complex task. Among many existing codes, SOLVEG is a one-dimensional numerical model to simulate multiphase transport through the unsaturated zone. Processes include tritium diffusion in both, gas and liquid phase, advection and dispersion for tritium in liquid phase, radioactive decay and equilibrium partitioning between liquid and gas phase. For its application with bare or vegetated (perennial vegetation or crops) soil surfaces and shallow or deep groundwater levels (contaminated or non-contaminated aquifer) the model has been adapted in order to include ground cover, root growth and root water uptake. The current work describes the approach and results of the modeling of a tracer test with tritiated water (7.3×108 Bq m−3) in a cultivated soil with an underlying 14 m deep unsaturated zone (non-contaminated). According to the simulation results, the soil’s natural attenuation process is governed by evapotranspiration and tritium re-emission. The latter process is due to a tritium concentration gradient between soil air and an atmospheric boundary layer at the soil surface. Re-emission generally occurs during night time, since at day time it is coupled with the evaporation process. Evapotranspiration and re-emission removed considerable quantities of tritium and limited penetration of surface-applied tritiated water in the vadose zone to no more than ∼1–2 m. After a period of 15 months tritium background concentration in soil was attained.

It is well-known that sediment composition strongly depends on grain size. A number of studies have tried to quantify this relationship focusing on the sand fraction, but only very limited data exists covering wider grain size ranges. Geologists have a clear conceptual model of the relation between grain size and sediment petrograpic composition, typically displayed in evolution diagrams. We chose a classical model covering grain sizes from fine gravel to clay, and distinguishing five types of grains (rock fragments, poly- and mono crystalline quartz, feldspar and mica/clay). A compositional linear process is fitted here to a digitized version of this model, by (i) applying classical regression to the set of all pairwise log-ratios of the 5-part composition against grain size, and (ii) looking for the compositions that best approximate the set of estimated parameters, one acting as slope and one as intercept. The method is useful even in the presence of several missing values. The linear fit suggests that the relative influence of the processes controlling the relationship between grain size and sediment composition is constant along most of the grain size spectrum.

This paper presents an approach conducive to an evaluation of the probability density function (pdf) of spatio-temporal distributions of concentrations of reactive solutes (and associated reaction rates) evolving in a randomly heterogeneous aquifer. Most existing approaches to solute transport in heterogeneous media focus on providing expressions for space–time moments of concentrations. In general, only low order moments (unconditional or conditional mean and covariance) are computed. In some cases, this allows for obtaining a confidence interval associated with predictions of local concentrations. Common applications, such as risk assessment and vulnerability practices, require the assessment of extreme (low or high) concentration values. We start from the well-known approach of deconstructing the reactive transport problem into the analysis of a conservative transport process followed by speciation to (a) provide a partial differential equation (PDE) for the (conditional) pdf of conservative aqueous species, and (b) derive expressions for the pdf of reactive species and the associated reaction rate. When transport at the local scale is described by an Advection Dispersion Equation (ADE), the equation satisfied by the pdf of conservative species is non-local in space and time. It is similar to an ADE and includes an additional source term. The latter involves the contribution of dilution effects that counteract dispersive fluxes. In general, the PDE we provide must be solved numerically, in a Monte Carlo framework. In some cases, an approximation can be obtained through suitable localization of the governing equation. We illustrate the methodology to depict key features of transport in randomly stratified media in the absence of transverse dispersion effects. In this case, all the pdfs can be explicitly obtained, and their evolution with space and time is discussed.